NEWARK, N.J. -- With a playoff berth locked up, all Devils coach Pete DeBoer wanted to see Tuesday against the Islanders was the same kind of workmanlike effort his team used to beat Chicago, Tampa Bay and Carolina in the past week.

DeBoer had few bones to pick with the Devils' loosey-goosey ways in the first period, but all in all, he didn't have much to complain about.

Playing without 30-goal scorer David Clarkson and using backup goalie Johan Hedberg instead of Martin Brodeur, the Devils played well enough to beat the New York Islanders 3-1 at Prudential Center. With Ottawa's loss to Carolina, the Devils are assured of finishing at least sixth in the Eastern Conference. Philadelphia's loss to the Rangers on Tuesday kept the Devils mathematically alive for fifth as well.

New Jersey still has games left to play Thursday at Detroit and Saturday at home against Ottawa.

"I liked how we played the second and third periods. I didn't like our first period," DeBoer said. "I thought we were a little loose, and we talked about it between the first and second. We tightened up our game, got the big power-play goal and I liked our game form that point forward."

Travis Zajac got the power-play goal 22 seconds into the second period. He called it a big goal for him "confidence-wise."

Zajac has played five straight games since missing 37 in a row with soreness in his surgically repaired Achilles tendon. He played over 20 minutes Tuesday, including 2:10 on the power play.

"I wanted to ramp his minutes up," DeBoer said of Zajac. "We got him up to 20 minutes. He played some power play, got a goal, and I think he's got his legs under him now. That was the goal before we get to the end of the season."

Patrik Elias had a goal and an assist, giving him 78 points in 77 career games against the Islanders. Zach Parise added two assists and Ilya Kovalchuk scored into an empty-net in the final minute for his 35th goal of the season.

However, the Devils defensive structure and discipline, especially over the final 40 minutes, is what allowed them to keep the Islanders from playing spoiler Tuesday. Hedberg faced only 20 shots -- including only four in the third period -- to win for the fifth time in six starts since the All-Star break. The Islanders didn't register their first shot on goal in the third until there was 4:20 remaining.

"They played their game to a T," Isles goalie Al Montoya said. "They kept us to the outside. Right off the bat we had a couple of chances, maybe our best chances, but they really just shut us down from there."

After Zajac gave the Devils the lead early in the second, they started to get pucks deep on the Islanders and come with a strong forecheck. The Devils were not whistled for a single minor penalty in the game, and the best chance the Islanders had was a breakaway by Michael Grabner in the second period that was thwarted by a standout defensive play from Mark Fayne.

It was basically textbook New Jersey hockey -- the exact style the Devils want to be playing going into the playoffs.

"We don't want to let our game slip here and come into the playoffs thinking we can just turn it on. It never works that way," Hedberg told NHL.com. "You have to use these games to fine tune everything and play with the urgency you want to have. If the other team doesn't show up and do that, it's obviously tougher, but you have to keep doing it and doing it. Even though it might get boring at times you have to plug away. We did that and that shows we're on the right path."

The win, however, came at a price because Devils center Jacob Josefson fractured his left wrist in the second period. Josefson, who was centering the fourth line, is expected to miss four to six weeks.

This is the second bad break for Josefson this season. He missed 37 games from Oct. 22 through Jan. 14 with a broken right clavicle.

Josefson was starting to get comfortable in his role and had three points in his previous five games.

"We all feel sorry for J.J. because he was playing really good and he was in unbelievable shape," Kovalchuk said. "But, those things happen in hockey. He just has to hang in there, work hard and he'll be back. A broken wrist is a tough one, but he's a tough kid."

The Devils gained the 2-1 lead courtesy of goals from Elias and Zajac.

Zajac's second goal of the season, and first on the power play, was the end result of some nifty passing from Marek Zidlicky to Elias to Parise. The Devils' captain fed Zajac from behind the net for a one-timer from the high slot.

"Zach made a good pass right in the wheelhouse," Zajac said.

Elias picked up the secondary assist, giving him 50 assists this season. He scored the Devils' first goal, his 26th of the season, on a one-timer from between the hash marks 1:18 into the first period. Petr Sykora collected the rebound to the right of the net and whipped a backhanded pass to Elias, who had room to quickly shoot the puck.

Islanders forward Matt Moulson scored his 35th goal of the season to make it 1-1 just 2:39 later, but after cleaning up their game during the first intermission the Devils got the goal from Zajac and went into lockdown mode.

It wasn't pretty, but this is not a team after style points. It never has been.

"We needed the points and we got the points," Parise told NHL.com. "Was it the best game we played? No, but we got it."